Fidelity of the surface code in the presence of a bosonic bath

We study the resilience of the surface code to decoherence caused by the presence of a bosonic bath. This approach allows us to go beyond the standard stochastic error model commonly used to quantify decoherence and error threshold probabilities in this system. The full quantum mechanical system-bath dynamics is computed exactly over one quantum error correction cycle. Since all physical qubits interact with the bath, space-time correlations between errors are taken into account. We compute the fidelity of the surface code as a function of the quantum error correction time. The calculation allows us to map the problem onto an Ising-like statistical spin model with two-body interactions and a fictitious temperature which is related to the inverse bath coupling constant. The model departs from the usual Ising model in the sense that interactions can be long ranged and can involve complex exchange couplings; in addition, the number of allowed configurations is restricted by the syndrome extraction. Using analytical estimates and numerical calculations, we argue that, in the limit of an infinite number of physical qubits, the spin model sustain a phase transition which can be associated to the existence of an error threshold in the surface code. An estimate of the transition point is given for the case of nearest-neighbor interactions.Comment: 15 pages, 5 figure

Improving the Efficiency of Stirling Engines for Use in Solar Distributed Electricity, Heating, and Cooling

Limiting solar power is the inability to cost effectively store energy. The most cost effective means to store solar energy is thermally in the ground, which can then be used for direct conversion to electricity. However, doing so is limited by a historically poor thermal efficiency of such engines. A novel Stirling engine is posed which more closely mimics a Carnot heat engine. It does this through the use of a new passive thermal ‘switch’ which permits heat flow into the expansion chamber of the Stirling engine only when the temperature of the chamber is above a desired value. Ideally heat would be added only at the end of the compression stroke and the beginning of the expansion stroke. Central to this thermal switch is the use of a vanadium dioxide (VO2) low mass heat exchanger internal to the expansion chamber. This low mass heat exchanger allows the film material to track and react to the temperature changes within the expansion chamber, permitting it to transfer heat only when needed. An adiabatic model of this enhanced solar Stirling engine is developed. Results indicate that the thermal efficiency can be nearly doubled, delivering a second law efficiency of over 0.6. Further, a year round overall efficiency accounting for losses in the Stirling engine and solar thermal collectors of 7% appears to be feasible when this engine is integrated with ground solar storage, providing the necessary power to meet loads in a low energy residence. Such results demonstrate promise for future application of this technology